Jeffrey Sanford Russell
University of Southern California
Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch.
Keywords Indefinite extensibility  Gunk  Contact puzzles
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Reprint years 2016
DOI 10.1080/0020174X.2015.1033006
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References found in this work BETA

Material Beings.Peter Van Inwagen - 1990 - Ithaca: Cornell University Press.
The Seas of Language.Michael Dummett - 1993 - Oxford University Press.
Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.

View all 41 references / Add more references

Citations of this work BETA

Infinitesimal Gunk.Lu Chen - 2020 - Journal of Philosophical Logic 49 (5):981-1004.
The World is the Totality of Facts, Not of Things.Agustín Rayo - 2017 - Philosophical Issues 27 (1):250-278.
Quantifier Variance and Indefinite Extensibility.Jared Warren - 2017 - Philosophical Review 126 (1):81-122.
The Metasemantics of Indefinite Extensibility.Vera Flocke - forthcoming - Tandf: Australasian Journal of Philosophy:1-18.
Intuitionistic Mereology.Paolo Maffezioli & Achille C. Varzi - 2021 - Synthese 198 (Suppl 18):4277-4302.

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